Biosignal and Biomedical Image Processing MATLAB based Applications - John L. Semmlow

topics. My only excuse for any omissions is that classroom experience with this approach seems to work: students end up with a working knowledge of a vast array of signal and image processing tools. A few of the classic or major books on these topics are cited in an Annotated bibliography at the end of the book. No effort has been made to construct an extensive bibliography or reference list since more current lists would be readily available on the Web.

TEXTBOOK PROTOCOLS

In most early examples that feature MATLAB code, the code is presented in full, while in the later examples some of the routine code (such as for plotting, display, and labeling operation) is omitted. Nevertheless, I recommend that students carefully label (and scale when appropriate) all graphs done in the problems. Some effort has been made to use consistent notation as described in Table 1. In general, lower-case letters n and k are used as data subscripts, and capital letters, N and K are used to indicate the length (or maximum subscript value) of a data set. In two-dimensional data sets, lower-case letters m and n are used to indicate the row and column subscripts of an array, while capital letters M and N are used to indicate vertical and horizontal dimensions, respectively. The letter m is also used as the index of a variable produced by a transformation, or as an index indicating a particular member of a family of related functions.* While it is common to use brackets to enclose subscripts of discrete variables (i.e., x[n]), ordinary parentheses are used here. Brackets are reserved to indicate vectors (i.e., [x1, x2, x3 , . . . ]) following MATLAB convention. Other notation follows standard conventions.

Italics (“) are used to introduce important new terms that should be incorporated into the reader’s vocabulary. If the meaning of these terms is not obvious from their use, they are explained where they are introduced. All MATLAB commands, routines, variables, and code are shown in the Courier typeface. Single quotes are used to highlight MATLAB filenames or string variables. Textbook protocols are summarized in Table 1.

I wish to thank Susanne Oldham who managed to edit this book, and provided strong, continuing encouragement and support. I would also like to acknowledge the patience and support of Peggy Christ and Lynn Hutchings. Professor Shankar Muthu Krishnan of Singapore provided a very thoughtful critique of the manuscript which led to significant improvements. Finally, I thank my students who provided suggestions and whose enthusiasm for the material provided much needed motivation.

*For example, m would be used to indicate the harmonic number of a family of harmonically related sine functions; i.e., fm(t) = sin (2 π m t).

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

TABLE 1 Textbook Conventions

mIndex of variable produced by transformation, or the index of

John L. Semmlow

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Contents

Preface

1Introduction

Typical Measurement Systems Transducers

Further Study: The Transducer Analog Signal Processing Sources of Variability: Noise

Electronic Noise Signal-to-Noise Ratio

Analog Filters: Filter Basics Filter Types

Filter Bandwidth Filter Order

Filter Initial Sharpness

Analog-to-Digital Conversion: Basic Concepts Analog-to-Digital Conversion Techniques

Quantization Error

Further Study: Successive Approximation Time Sampling: Basics

Further Study: Buffering and Real-Time Data Processing

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Data Banks

Problems

2Basic Concepts

Noise

Ensemble Averaging MATLAB Implementation

Data Functions and Transforms Convolution, Correlation, and Covariance

Convolution and the Impulse Response Covariance and Correlation

MATLAB Implementation

Sampling Theory and Finite Data Considerations Edge Effects

Problems

3Spectral Analysis: Classical Methods

Introduction

The Fourier Transform: Fourier Series Analysis Periodic Functions

Symmetry

Discrete Time Fourier Analysis Aperiodic Functions

Frequency Resolution

Truncated Fourier Analysis: Data Windowing Power Spectrum

MATLAB Implementation Direct FFT and Windowing

The Welch Method for Power Spectral Density Determination Widow Functions

Problems

4Digital Filters

The Z-Transform

Digital Transfer Function MATLAB Implementation

Finite Impulse Response (FIR) Filters FIR Filter Design

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Derivative Operation: The Two-Point Central Difference

Algorithm

MATLAB Implementation

Infinite Impulse Response (IIR) Filters

Filter Design and Application Using the MATLAB Signal

Processing Toolbox

FIR Filters

Two-Stage FIR Filter Design

Three-Stage Filter Design

IIR Filters

Two-Stage IIR Filter Design

Three-Stage IIR Filter Design: Analog Style Filters

Problems

5Spectral Analysis: Modern Techniques

Parametric Model-Based Methods MATLAB Implementation

Non-Parametric Eigenanalysis Frequency Estimation MATLAB Implementation

Problems

6Time–Frequency Methods

Basic Approaches

Short-Term Fourier Transform: The Spectrogram Wigner-Ville Distribution: A Special Case of Cohen’s Class Choi-Williams and Other Distributions

Analytic Signal MATLAB Implementation

The Short-Term Fourier Transform Wigner-Ville Distribution Choi-Williams and Other Distributions

Problems

7The Wavelet Transform

Introduction

The Continuous Wavelet Transform Wavelet Time—Frequency Characteristics MATLAB Implementation

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

The Discrete Wavelet Transform

Filter Banks

The Relationship Between Analytical Expressions and

Filter Banks

MATLAB Implementation

Denoising

Discontinuity Detection

Feature Detection: Wavelet Packets

Problems

8Advanced Signal Processing Techniques: Optimal and Adaptive Filters

Optimal Signal Processing: Wiener Filters MATLAB Implementation

Adaptive Signal Processing Adaptive Noise Cancellation MATLAB Implementation

Phase Sensitive Detection AM Modulation

Phase Sensitive Detectors MATLAB Implementation

Problems

9Multivariate Analyses: Principal Component Analysis and Independent Component Analysis

Introduction

Principal Component Analysis Order Selection

MATLAB Implementation Data Rotation

Principal Component Analysis Evaluation Independent Component Analysis

MATLAB Implementation Problems

10Fundamentals of Image Processing: MATLAB Image Processing Toolbox

Image Processing Basics: MATLAB Image Formats General Image Formats: Image Array Indexing

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Data Classes: Intensity Coding Schemes

Data Formats

Data Conversions

Image Display

Image Storage and Retrieval

Basic Arithmetic Operations

Advanced Protocols: Block Processing

Sliding Neighborhood Operations

Distinct Block Operations

Problems

11Image Processing: Filters, Transformations, and Registration

Spectral Analysis: The Fourier Transform MATLAB Implementation

Linear Filtering MATLAB Implementation

Filter Design Spatial Transformations

MATLAB Implementation Affine Transformations

General Affine Transformations Projective Transformations

Image Registration

Unaided Image Registration Interactive Image Registration

Problems

12Image Segmentation

Pixel-Based Methods Threshold Level Adjustment MATLAB Implementation

Continuity-Based Methods MATLAB Implementation

Multi-Thresholding Morphological Operations

MATLAB Implementation Edge-Based Segmentation

MATLAB Implementation Problems

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13Image Reconstruction

CT, PET, and SPECT Fan Beam Geometry

MATLAB Implementation Radon Transform

Inverse Radon Transform: Parallel Beam Geometry

Radon and Inverse Radon Transform: Fan Beam Geometry Magnetic Resonance Imaging

Basic Principles

Data Acquisition: Pulse Sequences Functional MRI

MATLAB Implementation

Principal Component and Independent Component Analysis Problems

Annotated Bibliography

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Annotated Bibliography

The following is a very selective list of books or articles that will be of value of in providing greater depth and mathematical rigor to the material presented in this text. Comments regarding the particular strengths of the reference are included.

Akansu, A. N. and Haddad, R. A., Multiresolution Signal Decomposition: Transforms, subbands, wavelets. Academic Press, San Diego CA, 1992. A modern classic that presents, among other things, some of the underlying theoretical aspects of wavelet analysis.

Aldroubi A and Unser, M. (eds) Wavelets in Medicine and Biology, CRC Press, Boca Raton, FL, 1996. Presents a variety of applications of wavelet analysis to biomedical engineering.

Boashash, B. Time-Frequency Signal Analysis, Longman Cheshire Pty Ltd., 1992. Early chapters provide a very useful introduction to time–frequency analysis followed by a number of medical applications.

Boashash, B. and Black, P.J. An efficient real-time implementation of the Wigner-Ville Distribution, IEEE Trans. Acoust. Speech Sig. Proc. ASSP-35:1611–1618, 1987. Practical information on calculating the Wigner-Ville distribution.

Boudreaux-Bartels, G. F. and Murry, R. Time-frequency signal representations for biomedical signals. In: The Biomedical Engineering Handbook. J. Bronzino (ed.) CRC Press, Boca Raton, Florida and IEEE Press, Piscataway, N.J., 1995. This article presents an exhaustive, or very nearly so, compilation of Cohen’s class of time-frequency distributions.

Bruce, E. N. Biomedical Signal Processing and Signal Modeling, John Wiley and Sons,

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

New York, 2001. Rigorous treatment with more of an emphasis on linear systems than signal processing. Introduces nonlinear concepts such as chaos.

Cichicki, A and Amari S. Adaptive Bilnd Signal and Image Processing: Learning Algorithms and Applications, John Wiley and Sons, Inc. New York, 2002. Rigorous, somewhat dense, treatment of a wide range of principal component and independent component approaches. Includes disk.

Cohen, L. Time-frequency distributions—A review. Proc. IEEE 77:941–981, 1989. Classic review article on the various time-frequency methods in Cohen’s class of time–frequency distributions.

Ferrara, E. and Widrow, B. Fetal Electrocardiogram enhancement by time-sequenced adaptive filtering. IEEE Trans. Biomed. Engr. BME-29:458–459, 1982. Early application of adaptive noise cancellation to a biomedical engineering problem by one of the founders of the field. See also Widrow below.

Friston, K. Statistical Parametric Mapping On-line at: http://www.fil.ion.ucl.ac.uk/spm/ course/note02/ Through discussion of practical aspects of fMRI analysis including pre-processing, statistical methods, and experimental design. Based around SPM analysis software capabilities.

Haykin, S. Adaptive Filter Theory (2nd ed.), Prentice-Hall, Inc., Englewood Cliffs, N.J., 1991. The definitive text on adaptive filters including Weiner filters and gradientbased algorithms.

Hyva¨rinen, A. Karhunen, J. and Oja, E. Independent Component Analysis, John Wiley and Sons, Inc. New York, 2001. Fundamental, comprehensive, yet readable book on independent component analysis. Also provides a good review of principal component analysis.

Hubbard B.B. The World According to Wavelets (2nd ed.) A.K. Peters, Ltd. Natick, MA, 1998. Very readable introductory book on wavelengths including an excellent section on the foyer transformed. Can be read by a non-signal processing friend.

Ingle, V.K. and Proakis, J. G. Digital Signal Processing with MATLAB, Brooks/Cole, Inc. Pacific Grove, CA, 2000. Excellent treatment of classical signal processing methods including the Fourier transform and both FIR and IIR digital filters. Brief, but informative section on adaptive filtering.

Jackson, J. E. A User’s Guide to Principal Components, John Wiley and Sons, New York, 1991. Classic book providing everything you ever want to know about principal component analysis. Also covers linear modeling and introduces factor analysis.

Johnson, D.D. Applied Multivariate Methods for Data Analysis, Brooks/Cole, Pacific Grove, CA, 1988. Careful, detailed coverage of multivariate methods including principal components analysis. Good coverage of discriminant analysis techniques.

Kak, A.C and Slaney M. Principles of Computerized Tomographic Imaging. IEEE Press, New York, 1988. Thorough, understandable treatment of algorithms for reconstruction of tomographic images including both parallel and fan-beam geometry. Also includes techniques used in reflection tomography as occurs in ultrasound imaging.

Marple, S.L. Digital Spectral Analysis with Applications, Prentice-Hall, Englewood Cliffs, NJ, 1987. Classic text on modern spectral analysis methods. In-depth, rigorous treatment of Fourier transform, parametric modeling methods (including AR and ARMA), and eigenanalysis-based techniques.

Rao, R.M. and Bopardikar, A.S. Wavelet Transforms: Introduction to Theory and Appli-

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.